WEALTH AND VOLATILITY
Jonathan Heathcote and Fabrizio PerriMinneapolis Fed
Federal Reserve Board, March 7, 2018
Sources of Business Cycles
• Great Recession brought back old idea: business cycles driven byself-fulfilling waves of optimism/pessimism
• What makes such waves more likely?
• Our idea: extent to which these waves can generate fluctuationsdepends on the level of household wealth
• Large and widespread decline in asset prices which occurred prior tothe crisis left many economies fragile and susceptible to aconfidence-driven recession
Median Real Household Net Worth (from SCF)
40,000
50,000
60,000
70,000
80,000
90,000
100,000
1989 1992 1995 1998 2001 2004 2007 2010 2013
SCF Survey Year
Note: Sample includes households with heads between ages 22 and 60.
2013
Dol
lars
Sunspot-driven fluctuations• Rise in expected unemployment→ consumers reduce demand→ firms reduce hiring→ higher unemployment
• For a wave of self-fulfilling pessimism to get started need highsensitivity of demand to expected unemployment
• High wealth:→ demand less sensitive to expectations (weak precautionarymotive)→ no sunspot-driven fluctuations
• Low wealth:→ demand more sensitive to expectations (strong precautionarymotive)→ sunspot-driven fluctuations
Household net worth in US in the long run
8.8
9.2
9.6
10.0
10.4
10.8
11.2
11.6
12.0
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Log of real net worth Trend
Wealth & GDP Volatility
.004
.006
.008
.010
.012
.014
.016
-.2
-.1
.0
.1
.2
60 65 70 75 80 85 90 95 00 05 10
Wealth
Volatility
Sta
ndar
d de
viat
ion
of G
DP
gro
wth
Household net w
orth (% dev. from
trend)
Note: Standard deviations of GDP growth are computed over 40-quarter rolling windows.Observations for net worth are averages over the same windows.
Outline
1. A tractable model of confidence driven recessions
2. Micro evidence on the link between wealth and precautionary motive
Simple dynamic monetary model
Key ingredients:
1. Imperfect unemployment insurance => precautionary motive forhouseholds => expected unemployment affects demand
2. Fixed nominal wage => demand affects unemployment
3. Central bank can offset weak demand by cutting nominal rate,except at ZLB
Agents
• Mass 1 of identical firms
• Mass 1 of identical households
• Each household contains mass 1 of potential workers
• Monetary authority
Representative firmPerfectly competitive, produces consumption good using indivisible labor
yt = nαt
where n is mass of workers hired and α < 1 (decreasing returns)Static profit maximization:
πt = maxnt≥0{ptyt − wtnt}
where pt is price of cons. relative to money, wt grows at constant rate γw
FOC: wt
pt= αnα−1
t
In equilibrium,ut = 1− nt
and thus
ut = 1−(αpt
wt
) 11−α
Households
• Infinitely-lived, enjoy two goods:
1. consumption, produced by firms
2. housing, aggregate endowment equal to 1
• Can save in housing and in govt. bonds (zero net supply)
• Unemployment risk + imperfect unemployment insurance withinperiod
=> tractable model of precautionary motive
Timing:
• All household members look for jobs
• If labor demand less than supply (nt < 1) jobs randomly rationed
• Within period, employed cannot transfer wages to unemployed familymembers
• => unemployed rely on savings to finance consumption• bonds are perfectly liquid• can only tap fraction ψ of home equity
• At end of period, household regroups, pools resources, decides onsavings for next period
Household solves
max{cw
t ,cut ,ht,bt}
E∞∑
t=0
(1
1 + ρ
)t
{(1− ut) log cwt + ut log cu
t + φ log ht−1}
s.t. budget constraints
ptcut ≤ ψph
t ht−1 + bt−1
ptcwt ≤ ψph
t ht−1 + bt−1 + wt
(1− ut) ptcwt + utptcu
t + pht (ht − ht−1) +
11 + it
bt ≤ (1− ut)wt + πt + bt−1
FOCs
Bonds1cw
t
11 + it
=1
1 + ρEt
[pt
pt+1
((1− ut+1)
cwt+1
+ut+1
cut+1
)]Extra real dollar tomorrow worth 1
cwt+1
to employed, 1cu
t+1to unemployed
Housing
pht
ptcwt=
11 + ρ
Et
[ph
t+1
pt+1
((1− ut+1ψ)
cwt+1
+ut+1ψ
cut+1
)+φ
ht
]
Real dollar’s worth of housing worth ψ to unemployed
Monetary authority
• Sets nominal rate it
• Follows rule of form
it = iCB(ut) = max {(1 + γw) (1 + ρ− κut)− 1, 0}
• κ controls how aggressively central bank cuts rates whenunemployment goes up
• Will consider passive (κ small) and aggressive (κ large) policies
Equilibrium
An equilibrium is a probability distribution over {ut, nt, yt, πt, cwt , c
ut , ht, bt}
and{
it, pt, pht ,wt
}that satisfies, at each date t
1. Household and firm optimality2. The policy rule it = iCB(ut)
3. Market Clearing:
(1− ut) cwt + utcu
t = yt
ht = 1
bt = 0
Steady States• Real variables and interest rate are constant, prices grow at rate γw
• There is always a full employment steady state in which
u = 0,
y = 1,
1 + i = (1 + ρ)(1 + γw),
ph
p=
φ
ρ.
• This is the efficient allocation
• Whether other steady states exist depends on level of householdliquid wealth, and monetary policy aggressivity
Steady State Asset Prices
• Put aside for a moment the monetary rule
• For any possible steady state unemployment rate u, what dooptimization and market clearing imply for real house prices and theequilibrium interest rate?
• Answer depends on parameters that determine household liquidwealth: ψ, φ, ρ
Perfect Risk Sharing Steady States
• If ψ(φρ ) > 1 then risk sharing is perfect is any steady state:
1 + i = (1 + ρ)(1 + γw)
ph
p=
φ
ρ(1− u)α
Imperfect Risk Sharing Steady States
• If ψ(φρ ) < 1 then risk sharing is imperfect in any steady state
• Real house prices are given by
ph
p=
φ
ρ(1− u)α︸ ︷︷ ︸
fundamental component
× u + φ
ψ φρu +(
1 +(ψ φρ − 1
)u)φ︸ ︷︷ ︸
liquidity component
• Liquidity component > 1
Real House Prices and Unemployment
Unemployment Rate (%)0 5 10 15 20
Rea
l Hou
se P
rices
1.8
1.85
1.9
1.95
2
2.05
Imperfect Risk Sharing Steady States
• If ψ(φρ ) < 1 then household optimality and market clearing imply
i = i(u) = (1 + ρ) (1 + γw)
u + φ
u(
1 + ρψ − φ
)+ φ
− 1
• i(u) derived from FOC for bonds, imposing market clearing andsteady state house price expression
• 1 + i(0) = (1 + ρ)(1 + γw)
• i(u) is a decreasing and convex function of u
Steady StatesA steady state is a pair (i, u) satisfying i = i(u) and i = iCB(u)
Unemployment Rate (%)0 2 4 6 8 10 12 14 16 18
Nom
inal
Inte
rest
Rat
e (%
)
-1
0
1
2
3
4
5
Steady States
Bond Market Clearing, i(u)
Monetary Rule, iCB(u)
Characterizing Equilibria
• Different sorts of equilibria are possible depending on:
1. Level of liquid wealth, which determines how fast i(u) declines with u2. Monetary policy, which determines how fast iCB(u) declines with u
• High liquid wealth: ψ > ρ(1+ρ)(1+γw)(1+φ)−1
• High liquid wealth⇒ i(u) > 0 for all u
• Aggressive monetary rule: κ > (1 + ρ)
(1−ψφ
ρψφρ
)• Aggressive rule⇒ iCB(u) falls faster than i(u) at u = 0
Dynamics Around Full Employment
• Definition: A steady state is locally stable (unstable) if there do (not)exist perfect foresight paths that converge to it
• Result: If monetary policy is passive (aggressive) then the fullemployment steady state is locally stable (unstable)
• Implication: An aggressive policy rules out temporaryconfidence-driven fluctuations
• Intuition: Aggressive Fed promises to cut rate more than required tosupport demand⇒ temporary recession not possible
Policy Aggressivity and Local Stability
Unemployment Rate (%)0 2 4 6 8 10 12 14 16 18
Nom
inal
Inte
rest
Rat
e (%
)
-1
0
1
2
3
4
5
Bond Market Clearing, i(u)
iCB(u), Aggressive
iCB(u), Passive
Sunspot path
High Liquidity
• Result: If liquid wealth is high and policy is aggressive, fullemployment is only equilibrium
• Intuition: High liquid wealth => weak precautionary motive => i > 0 inany steady state
• => Aggressive central bank can promise low enough policy rate torule out positive unemployment steady states
• Aggressive CB can also rule out temporary recessions
• Implication: Central bank in high liquid wealth environment should beaggressive
Low Liquidity Case
Unemployment Rate (%)0 2 4 6 8 10 12 14 16 18
Nom
inal
Inte
rest
Rat
e (%
)
-1
0
1
2
3
4
5
Bond Market Clearing, i(u)
iCB(u), Aggressive
iCB(u), Passive
Sunspot paths
Positive Unemployment SS, u+
Low Liquidity
• Result: Under an aggressive policy, a new steady state emergeswith u > 0 and i = 0
• Intuition: Low liquid wealth => poor insurance within household
• If households expect persistent unemployment, strong precautionarymotive and weak demand
• => A depressed-demand stagnation ZLB steady state emerges
• Result: The depressed steady state is locally stable
• Intuition: At the ZLB the CB is not responding aggressively enoughto fluctuations in unemployment
Policy Dilemma With Low Liquid Wealth
• Low wealth opens the door to rich macroeconomic volatility
• No simple policy fix: bad outcomes possible whether central bankpassive or aggressive
• Aggressive central bank: Confidence shocks can lead to stagnationsteady state
• Passive central bank: Confidence shocks can lead to temporaryrecessions
• Unemployment insurance can be an effective policy:
• Weakens impact of expected unemployment on precautionary motive
• Can eliminate stagnation steady state
Figure: Global Dynamics with Low Liquid Wealth
Great Recession Calibration• IES = 1/3⇒ CRRA = 3⇒ strong precautionary motive
• ρ = 0.025⇒ real interest rate at full employment is 2.5%
• γw = 0.02⇒ steady state inflation is 2.0%
• φ = 0.075→ φ = 0.05 in 2008
• ⇒ full employment house value to consumption declines from 3 to 2
• Shifts economy from high liquid wealth to low liquid wealth regime
• κ = 1.5⇒ midpoint of Taylor 1993 and 1999 coefficients
• ψ = 0.33⇒ cu/cw = 0.76 when recession hits
• Given κ, need ψ < 0.37 for policy to be passive
• ⇒ can construct sunspot shock to generate 6% jump in unemploymentrate in 2009
Interpreting the Great Recession
• Decline in φ reduced ph pushing economy into low liquid wealthregion
• Not inherently recessionary but creates vulnerability to a confidenceshock
• Collective loss of confidence (collapse of Lehman?) triggeredsunspot shock taking us to u > 0
• Gradual recovery in which demand stimulus from expected growthbalanced by strong precautionary motive plus rising rates
• Fed could have tried more aggressive policy, but could not haveruled out a permanent slump
Other Models of the Lower Bound
Contrast with existing ZLB models, of which there are two types
1. Exogenous change in preferences to β > 1 drives temporary declinein real rate (e.g., Eggertsson & Woodford, 2003)
• Shock hard to interpret• Shock has to be temporary• We don’t need any exogenous shocks
2. Flip to nominal wage and price deflation (e.g., Benhabib,Schmitt-Grohe & Uribe, 2001, 2002)
• Deflationary steady state has π = −ρ• But ZLB experience in US involved low r, not π < 0
Micro Evidence for the Mechanism
• Key mechanism: Elasticity of expenditures wrt unemployment risk islarger when wealth is low (for precautionary motives)
• Natural test: Did wealth-poor households reduce expenditures morethan rich households as unemployment risk rose during the GreatRecession?
Micro Survey Data
• Use both the CEX (higher frequency) and the PSID (longer panel)
• Focus on households of working age
• Divide sample by household wealth (net financial wealth plus homeequity) relative to avg. expenditure
• Compare panel change in saving to income ratio for the high v/s lowwealth groups
• Do we see larger rise in saving rates for the low wealth group at thestart of the recession?
Surveys versus NIPA
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
A. Per capita consumption expenditures
2004
=1
NIPA
CES
PSID
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
B. Per capita disposable income
2004
=1
NIPA
CES
PSID
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
C. Median household net worth
2004
=1
SCF
CES
PSID
Characteristics of Rich versus PoorTable 1. Characteristics of the wealth rich and the wealth poor, 2006
PSID CES
Poor Rich Poor Rich
Sample size 3446 2523 1915 1960
Mean age of head37.9
(0.21)
47.1
(0.21)
40.2
(0.25)
46.4
(0.24)
Heads with college (%)21.3
(0.86)
36.5
(1.1)
24.8
(1.1)
39.4
(1.2)
Mean household size2.45
(0.04)
2.72
(0.03)
2.84
(0.04)
2.79
(0.04)
Mean household net worth (current $)11,931
(879)
619,831
(49,388)
11,967
(1,155)
338,535
(12,644)
Median household net worth5,000
(476)
265,000
(6,602)
1,800
(294)
187,102
(4,893)
Per capita disposable income15,028
(256)
28,475
(667)
18,739
(334)
30,184
(593)
Per capita consumption expenditure9,831
(177)
13,101
(250)
9,185
(232)
10,858
(188)
Consumption rate (%)65.8
(0.90)
46.0
(0.86)
49.0
(1.18)
36.0
(0.66)
Note: Bootstrapped standard errors are in parentheses.
6.5 Changes in Consumption Rates: Rich versus Poor Households
Figure 11 contains the key finding of this section. The figure plots changes in consumption rates
in both the PSID (Panel A) and the CES (Panel B). Around the onset of the recession both
data sets reveal a decline in the consumption rate of the poor that is significantly larger than the
corresponding decline for the rich.14
Before concluding that the large fall in the consumption rate of the poor (relative to the rich)
is due to the poor having a stronger precautionary motive, we consider two alternative possible
explanations. The first is that the poor cut their consumption more because they suffered larger
wealth losses. The second is that the poor cut their consumption more because their income
prospects deteriorated more than those of the rich.
To evaluate the first alternative explanation we exploit the fact that households in the PSID
14Consumption rate declines in the CES (Panel B) appear to be smaller than in the PSID. We conjecture that thisprimarily reflects the fact that the CES consumption rate changes are computed over 9 month intervals, while thePSID changes are recorded over 2 year intervals.
33
Wealth and Changes in Saving Rates
-4
-2
0
2
4
6
8
10
12
2004-2006 2006-2008 2008-2010 2010-2012
Cha
nge
in s
avin
g ra
te (p
p)
A. PSID over time
Rich
Poor
-4
-2
0
2
4
6
8
10
12
Q1 Q2 Q3 Q4 Q5
2004-2006
2006-2008
B. PSID by Net Worth Quintile
-1
0
1
2
3
4
2005-06 2006-07 2007-08 2008-09 2009-10 2010-11 2011-12 2012-13
Cha
nge
in s
avin
g ra
te (p
p)
C. CES over time
Rich
Poor
-1
0
1
2
3
4
1 2 3 4 5
Net Worth Quintiles
2004-2006
2006-2008
D. CES by Net Worth Quintile
Years
Are Other Factors Driving This?
-4
-2
0
2
4
6
8
10
12
2004 2006 2008 2010 2012
Cha
nge
from
200
6 sa
ving
rat
e (p
p)
A. Saving Rates
Rich
Poor
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
2004 2006 2008 2010 2012
Rat
io to
200
6 In
com
e
B. Disposable Income
Rich
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
2004 2006 2008 2010 2012R
atio
to 2
006
expe
nditu
res
C. Consumption Expenditures
Rich
Poor
Poor
Poor
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
2004 2006 2008 2010 2012
Diff
eren
ce fr
om 2
006
rate
(pp
)
D. Unemployment Rate
Rich
Poor
-250
-200
-150
-100
-50
0
50
100
2004 2006 2008 2010 2012
Diff
eren
ce fr
om 2
006
ratio
(pp
)
E. Net Worth to Income Ratio
Rich
Conclusions
• Model in which macroeconomic stability threatened by low liquidwealth
• Great Recession: Decline in home values left economy vulnerable towave of pessimism
• Macro evidence of a link between level of wealth and aggregatevolatility
• Micro evidence that low wealth households increased saving mostsharply
• Can evaluate effectiveness of policies geared toward stabilization ofthese fluctuations